I've participated in Burning Man four times over the past ten years and missed the first week of classes each year (twice as an undergrad, twice as a graduate student). The amount of notice and detail I would give each professor depended on the class. For large general-education courses, I would write a week ahead of time saying I had a time conflict and would miss the first week, but would be sure to make up any missed notes/coursework and attend the following week. For smaller seminar courses or anything graduate-level, I would give more detail. Being in the social sciences, generally I felt comfortable sharing that I was attending Burning Man (as a valuable social experiment but also valuable to me, personally). Again, assuring the professor that I was eager and excited for their course and that I would make up any missed work always worked for me. Of course, I'm in Ohio, so this situation may be more novel for professors than, say, those at UCBerkeley.